Equilibrium Strategies In M/M/1 Priority Queues With Variable Service Rate

Queuing theory penetrates into all aspects of daily life.By studying the queuing model suitable for real life,it can not only provide customers with services more in line with their needs,but also help businesses stand out in the market competition and obtain higher profits.Therefore,it can be made more reasonable by optimizing the resource allocation of both parties.This thesis considers the M/M/1 queueing system with preemptive priority and variable service rate,and studies the equilibrium strategy when it satisfies the social optimization and individual optimization under the observable and unobservable conditions respectively.The main research contents are as follows:Firstly,it introduces the significance of queue theory in real life,the research status at home and abroad,and the main research content and structure of the whole thesis.Secondly,some basic knowledge of queuing theory is introduced to pave the way for the follow-up content.Then,the calculation methods of strategies in classical M/M/1 queueing system and M/M/1queueing system with priority are introduced when individual optimization and social optimization are satisfied under observable and unobservable conditions respectively.Then,on the basis of these two queuing systems,the M/M/1 queuing system with preemptive priority and variable service rate is considered.When customers enter the system,they will have three options: leaving the system directly,joining the priority queue to obtain high-speed service and joining the ordinary queue to obtain low-speed service.When customers are not observable,the joint probability is obtained for customers choosing to wait in the queue and customers choosing to join the priority queue.In the case of customer observability,the thresholds of the number of people in the priority queue and the ordinary queue are obtained.If the number of people observed by customers exceeds the total threshold,they will choose to leave directly.Finally,the optimal strategies in the two cases are further demonstrated by numerical simulation of the model,and the future research direction is given.13 pictures,2 tables,65 references...